The present invention relates to an apparatus and a method that are applied to a measurement of a jitter of, for example, a microprocessor clock, and are used for estimating a fluctuation of a zero crossing interval of an input signal and a peak jitter (period jitter), particularly for estimating a worst value of peak jitter and its occurrence probability.
A clock frequency of microprocessor is doubled in every forty months. The shorter a clock period is, the more severe jitter measurement is required. This is because a timing error in the system operation must be avoided.
Incidentally, there are two types of jitters, i.e., a period jitter and a timing jitter. A period jitter becomes a problem since, in a computer clock for example, an upper limit of its operation frequency is determined by a period jitter. As shown in FIG. 1A, in a jitter-free ideal clock signal, for example, an interval Tint between adjacent rising points is constant as indicated by a dotted line waveform, and in this case a period jitter is zero. In an actual clock signal, a rising edge fluctuates from an arrow toward leading side or trailing side, i.e., an interval Tint between adjacent rising points fluctuates, and this fluctuation of the interval is a period jitter. For example, in the case of a sine wave that does not have a rectangular waveform like a clock signal, a fluctuation of an interval Tint between zero-crossing points is also a period jitter. A period jitter becomes a problem of computer clocks.
On the other hand, a timing jitter is defined as the timing deviation from an ideal point in, for example, data communication. As shown in FIG. 1B, when a jitter-free square waveform is assumed to be a dashed line waveform, a deviation width xcex94xcfx86 of an actual rising point (solid line) from a normal rising point (dashed line) is a timing jitter in the case of a jittery square waveform.
A conventional measurement of a period jitter is performed by a time interval analyzer (hereinafter, this measuring method is referred to as a time interval method or a TIA method). This is shown in xe2x80x9cPhase Digitizing Sharpens Timing Measurementsxe2x80x9d by David Chu, IEEE Spectrum, pp. 28-32, 1988, and xe2x80x9cTime Domain Analysis and Its Practical Application to the Measurement of Phase Noise and Jitterxe2x80x9d, by Lee D. Cosart et al., IEEE Trans. Instrum. Meas., vol.46, pp. 1016-1019, 1997. This time interval method is a method in which zero-crossing points of a signal under test are counted, an elapsed time is measured, and a time fluctuation between zero-crossing points is estimated to obtain a period jitter. In this time interval method, it takes a long time to perform those measurements since data present between zero-crossings are not utilized for the measurements.
There is a method, as a conventional timing jitter measurement, in which a timing jitter is measured in frequency domain using a spectrum analyzer. Since, in this method, a low frequency range is swept to measure a phase noise spectrum, it takes approximately 10 minutes or so for the measurement.
From those view points, inventors of the present invention have proposed a method of measuring a jitter as described below in an article entitled xe2x80x9can application of an instantaneous phase estimating method to a jitter measurementxe2x80x9d in a technical report xe2x80x9cProboxe2x80x9d pp. 9-16 issued by Probo Editorial Room of ADVANTEST CORPORATION, Nov. 12, 1999.
That is, as shown in FIG. 2, an analog clock waveform from a PLL circuit under test (Phase locked loop) 11 is converted into a digital clock signal xc(t) by an digital-analog converter 12, and the digital clock signal xc(t) is supplied to a Hilbert pair generator 14 acting as analytic signal transforming means 13, where the digital clock signal xc(t) is transformed into an analytic signal zc(t).
Now, a clock signal xc(t) is defined as follows.
xc(t)=Ac cos(2xcfx80fct+xcex8c+xcex94xcfx86(t))
The Ac and the fc are nominal values of amplitude and frequency of the clock signal respectively, the xcex8c is an initial phase angle, and the xcex94xcfx86(t) is a phase fluctuation that is called a phase noise.
The clock signal xc(t) is Hilbert-transformed by a Hilbert transformer 15 in the Hilbert pair generator 14 to obtain the following equation.
{circumflex over (x)}c(t)=H[xc(t)]=Ac sin(2xcfx80fct+xcex8c+xcex94xcfx86(t))
Then, an analytic signal zc(t) having xc(t) and {circumflex over (x)}c(t) as a real part and an imaginary part, respectively is obtained as follows.                                           z            c                    ⁡                      (            t            )                          =                  xe2x80x83                ⁢                                            x              c                        ⁡                          (              t              )                                +                                                    x                ^                            c                        ⁡                          (              t              )                                                              =                  xe2x80x83                ⁢                              A            c                    ⁢                      cos            (                                          2                ⁢                π                ⁢                                  xe2x80x83                                ⁢                                  f                  c                                ⁢                t                            +                              θ                c                            +                              Δφ                ⁡                                  (                  t                  )                                            +                              j                ⁢                                  xe2x80x83                                ⁢                                  A                  c                                ⁢                                  sin                  ⁡                                      (                                                                  2                        ⁢                        π                        ⁢                                                  xe2x80x83                                                ⁢                                                  f                          c                                                ⁢                        t                                            +                                              θ                        c                                            +                                              Δφ                        ⁡                                                  (                          t                          )                                                                                      )                                                                                          
From this analytic signal zc(t), an instantaneous phase "THgr"(t) of the clock signal xc(t) can be estimated by the instantaneous phase estimator 16 as follows.
"THgr"(t)=[2xcfx80fct+xcex8c+xcex94xcfx86(t)] mod 2xcfx80
A linear phase is removed from this instantaneous phase "THgr"(t) by a linear phase remover 17 to obtain a phase noise waveform xcex94xcfx86(t). That is, in the linear phase remover 17, a continuous phase converting part 18 applies a phase unwrap method to the instantaneous phase "THgr"(t) to obtain a continuous phase xcex8(t) as follows.
xcex8c(t)=2xcfx80fct+xcex8c+xcex94xcfx86(t)
The phase unwrap method is shown in xe2x80x9cA New Phase Unwrapping Algorithmxe2x80x9d by Jose M. Tribolet, IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-25, pp. 170-177, 1977 and in xe2x80x9cOn Frequency-Domain and Time-Domain Phase Unwrappingxe2x80x9d by Kuno P. Zimmermann, Proc. IEEE. vol. 75, pp. 519-520, 1987.
A linear phase [2xcfx80fct+xcex8c] of a continuous phase xcex8(t) is estimated by a linear phase evaluator 19 using a linear trend estimating method. This estimated linear phase [2xcfx80fct+xcex8c] is subtracted from the continuous phase xcex8(t) by a subtractor 21 to obtain a variable term xcex94xcfx86(t) of the instantaneous phase "THgr"(t), i.e., phase noise waveform as follows.
xcex8(t)=xcex94xcfx86(t)
The phase noise waveform xcex94xcfx86(t) thus obtained is inputted to a peak-to-peak detector 22, where a difference between the maximum peak value max (xcex94xcfx86(k)) and the minimum peak value min (xcex94xcfx86(1)) of the xcex94xcfx86(t) is calculated to obtain a peak value xcex94xcfx86pp of timing jitters as follows.       Δφ    pp    =                    max        k            ⁢              (                  Δφ          ⁡                      (            k            )                          )              -                  min        l            ⁢              (                  Δφ          ⁡                      (            l            )                          )            
In addition, the phase noise waveform xcex94xcfx86(t) is inputted to a root-mean-square detector 23, where a root-mean-square value of the phase noise waveform xcex94xcfx86(t) is calculated using following equation to obtain a root-mean-square value xcex94xcfx86RMS of timing jitters.       Δφ    RMS    =                    1        N            ⁢                        ∑                      k            =            0                                N            -            1                          ⁢                  xe2x80x83                ⁢                              Δφ            2                    ⁡                      (            k            )                              
A method is called the xcex94xcfx86 method since it estimates a peak value of timing jitters and/or a root-mean-square value of timing jitters from the phase noise waveform xcex94xcfx86(t). According to the xcex94xcfx86 method, a jitter measurement can be performed in a test time of 100 millisecond order since measuring points are not limited to zero-crossing points. Further, in FIG. 2, the analytic signal transforming means 13, the instantaneous phase estimator 16 and the linear phase remover 17 compose phase noise detecting means 25.
As mentioned above, it is important, for example in manufacturing computers, to know whether or not the computer can operate even in the worst peak value case of period jitter in the operation clock, namely in the worst case condition that has both the maximum time interval between adjacent rising edges of a clock and the minimum time interval between adjacent rising edges of a clock. From this point of view, it is requested to measure the worst period jitter value of a microprocessor to be used in a computer and to perform a test in a short time to see whether or not the microprocessor is defective based on whether the worst period jitter value is equal to or less than a predetermined value.
However, according to the conventional time interval method, a time interval between adjacent zero-crossings is measured to estimate its fluctuation, and each period jitter value occurs as a random variable. Therefore, when the worst value of period jitters is measured, an accurate value cannot be obtained unless period jitters of a signal under test are measured for a long time. Therefore, in the conventional method, it is actually difficult to test, for example, whether or not a manufactured microprocessor is a non-defective chip having the worst period jitter value of a clock equal to or less than a predetermined value.
In addition, it is effective as a factor for evaluating the product reliability of a microprocessor to estimate an occurrence probability of the worst period jitter value of its clock. However, in the conventional method, it is difficult to obtain a peak value of period jitter at high speed, and hence the occurrence probability of a peak value of period jitter has not even been defined.
It is another object of the present invention to provide an apparatus for and a method of measuring a peak jitter that can estimate an occurrence probability of each period jitter value in relatively short time.
It is another object of the present invention to provide an apparatus for and a method of measuring a peak jitter that can obtain an occurrence probability of each period jitter value in relatively short time.
Prior to the description of the present invention, the principle of the present invention will be explained. In a narrow-band random process {J(nT)}, when a certain instantaneous value follows Gaussian distribution, a set of its peak values, namely a set of the maximum values of absolute values of J(nT), i.e., {max[abs(J(nT))]} becomes closer to Rayleigh distribution when a degree of freedom n (the number of samples) is made large. This principle is explained in, for example, xe2x80x9cRandom Data: Analysis and Measurement Procedurexe2x80x9d by J. S. Bendat and A. G. Piersol, 2 nd ed, P542, John Wiley and Sons, Inc, 1986, or in xe2x80x9cAn Introduction to Random Vibrations, Spectral and Wavelet Analysisxe2x80x9d by D. E. Newland, P90xcx9c92, Longman Scientific and Technical, 1993.
FIG. 3 shows a power spectrum obtained by performing fast-Fourier-transforming on the clock waveform of a microprocessor of a PC (personal computer). FIG. 3A shows a case of quiet mode, i.e., a case of non-active state of a microprocessor. In the non-active state, when the personal computer waits for a user instruction, only a PLL circuit outputting a clock signal activated giving reference clock edges from a reference clock generator wherein the best state that the clock is not influenced by the operation of the personal computer is provided. FIG. 3B shows a case of noisy mode, i.e., a case of extremely active state of a microprocessor. In the noisy mode, a level 2 memory, system and core buses, and branch predictor units in a personal computer are all in full activated, wherein a state that the clock is most influenced by the operation of the personal computer is provided.
In either FIG. 3A or 3B, a line spectrum of the clock appears at 400 MHz (fundamental frequency of the clock), and random phase noises are observed in the sidebands close to 400 MHz as a central frequency. This shows a presence of narrow-band random data.
On the other hand, a probability density function (histogram) of a clock jitter follows Gaussian distribution as shown in FIG. 4. FIG. 4A shows a case of the quiet mode, and FIG. 4B shows a case of the noisy mode. Since those random phase noises are present, and since those random phase noises, i.e., instantaneous values of clock jitter follow Gaussian distribution, a set of peak period jitter values (peak jitter) of the clock, i.e., {max[abs(J(nT))]} follows Rayleigh distribution.
It is known that a probability density function of Rayleigh distribution P(Jp) is given by the following equations.                                                                         P                ⁡                                  (                                      J                    p                                    )                                            =                                                                    J                    P                                                        σ                    J                    2                                                  ⁢                                  exp                  ⁡                                      (                                          -                                                                        J                          P                          2                                                                          2                          ⁢                                                      σ                            J                            2                                                                                                                )                                                                                                                          J                p                             greater than               0                                                            0                                                              J                r                             greater than               0                                                          (        1        )            
In this case, "sgr"j is a root-mean-square value of peak values Jp.
In addition, it is also known that a probability that a peak value Jp becomes larger than a certain value Ĵp (right-tail probability) is given by the following equation.                                                                                           P                  r                                ⁡                                  (                                                            J                      p                                         greater than                                                                   J                        ^                                            P                                                        )                                            =                              xe2x80x83                            ⁢                                                ∫                                                            J                      ^                                        p                                    ∞                                ⁢                                                      P                    ⁡                                          (                                              J                        p                                            )                                                        ⁢                                      xe2x80x83                                    ⁢                                      ⅆ                                          J                      P                                                                                                                                              =                              xe2x80x83                            ⁢                              exp                ⁡                                  (                                      -                                                                                            J                          ^                                                P                        2                                                                    2                        ⁢                                                  σ                          J                          2                                                                                                      )                                                                                        (        2        )            
As clearly explained above, a set of peak period jitter values {max[abs(Jp)]} follows Rayleigh distribution. Rayleigh distribution is described in xe2x80x9cFundamentals of Statistical Signal Processing: Detection Theoryxe2x80x9d by S. M. Kay, Prentice-Hall, Inc. 1998, PP. 30xcx9c31.
Therefore, the equations (1) and (2) can be applied to a set of peak period jitter values {max[abs(Jp)]}. Consequently, if a positive maximum value (zero-peak value) of peak jitter fluctuation is Ĵpk. a probability that a period jitter becomes larger than Ĵpk is given by the following equation.                                                                                           P                  r                                ⁡                                  (                                                            J                      p                                         greater than                                                                   J                        ^                                            pk                                                        )                                            =                                                ∫                                                            J                      ^                                        pk                                    ∞                                ⁢                                                      P                    ⁡                                          (                                              J                        p                                            )                                                        ⁢                                      xe2x80x83                                    ⁢                                      ⅆ                                          J                      p                                                                                                                                              =                              exp                ⁡                                  (                                      -                                                                                            J                          ^                                                pk                        2                                                                    2                        ⁢                                                  σ                          J                          2                                                                                                      )                                                                                        (        3        )            
The standard deviation of Ĵpk is given by the following equation.                               σ                      J            pk                          =                                                            4                -                π                            2                                ⁢                      σ            J                                              (        4        )            
That is, when Ĵpk is defined as the worst peak value of period jitter, and a root-mean-square value "sgr"j of the jitters of a signal under test and Ĵpk are measured, a probability that a period jitter of the signal under test exceeds the worst peak value Ĵpk can be estimated. It can also be estimated that the smaller the probability is, the higher the reliability of a product to be processed by the signal under test is. An aspect of the present invention is to estimate a probability of a peak value of period jitter of an input signal based on the above consideration.
Incidentally, in FIG. 1B, when a clock rises at time point 0 (zero) with the maximum delay deviation from an ideal rising point, and rises at next time point T with the maximum lead deviation from the ideal rising point, i.e., when a timing jitter xcex94xcfx86(0) at time point 0 is the negative maximum value xe2x88x92xcex94xcfx86max, and a timing jitter xcex94xcfx86(T) at time point T is the positive maximum value +xcex94xcfx86max, a peak jitter becomes the worst value in the positive direction as shown below.
Jpxe2x80x2+=xcex94xcfx86maxxe2x88x92(xe2x88x92xcex94xcfx86max)=2xcex94xcfx86maxxe2x80x83xe2x80x83(5)
Similarly, when a timing jitter xcex94xcfx86(0) at time point 0 is the positive maximum value +xcex94xcfx86max, and a timing jitter xcex94xcfx86(T) at time point T is the negative maximum value xe2x88x92xcex94xcfx86max, a peak jitter becomes the worst value in the negative direction as shown below.
Jpxe2x80x2xe2x88x92=xcex94xcfx86maxxe2x88x92xcex94xcfx86max=xe2x88x922xcex94xcfx86maxxe2x80x83xe2x80x83(6)
Therefore, the maximum peak-to-peak value of period jitter, i.e., the worst value Jxe2x80x2pp of period jitter is given by the equation below.
Jppxe2x80x2=Jpxe2x80x2+xe2x88x92Jpxe2x80x2xe2x88x92=xcex94xcfx86maxxe2x80x83xe2x80x83(7)
Further, in general, the maximum value of period jitter in the positive direction is equal to the maximum value of period jitter in the negative direction.
From the relationship described above, in a second aspect of the present invention, the maximum value of timing jitter xcex94xcfx86max is estimated to make it possible to estimate the worst peak value or the worst value of period jitter in a short time.
According to one aspect of the present invention, an input signal is transformed into a complex analytic signal, and an instantaneous phase of the analytic signal is obtained. A linear phase is removed from the instantaneous phase to obtain a phase noise waveform, and the maximum value of absolute value of the phase noise waveform is obtained. And the maximum value is multiplied by 2 to obtain the worst peak value of period jitter, or the maximum value is multiplied by 4 to obtain the worst value of period jitter of the input signal.
According to another aspect of the present invention, a phase noise waveform is obtained similarly to the previous case. The worst peak value of the input signal is estimated from the phase noise waveform. In addition, a root-mean-square jitter of period jitters of the input signal is obtained from the phase noise waveform. A probability of period jitter of the input signal is obtained from the worst peak value and the root-mean-square jitter.